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The head loss Δh (or h f) expresses the pressure loss due to friction in terms of the equivalent height of a column of the working fluid, so the pressure drop is =, where: Δh = The head loss due to pipe friction over the given length of pipe (SI units: m); [b]
The friction loss is customarily given as pressure loss for a given duct length, Δp / L, in units of (US) inches of water for 100 feet or (SI) kg / m 2 / s 2. For specific choices of duct material, and assuming air at standard temperature and pressure (STP), standard charts can be used to calculate the expected friction loss.
The Borda–Carnot loss equation is only valid for decreasing velocity, v 1 > v 2, otherwise the loss ΔE is zero – without mechanical work by additional external forces there cannot be a gain in mechanical energy of the fluid. The loss coefficient ξ can be influenced by streamlining.
In total loss, endwall losses form the fraction of secondary losses given by Gregory-Smith, et al., 1998. Hence secondary flow theory for small flow-turning fails. Correlation for endwall losses in an axial-flow turbine is given by: ζ = ζ p + ζ ew ζ = ζ p [ 1 + ( 1 + ( 4ε / ( ρ 2 V 2 /ρ 1 V 1) 1/2) ) ( S cos α 2 - t TE)/h ]
[1] [2] [3] A key question is the uniformity of the flow distribution and pressure drop. Fig. 1. Manifold arrangement for flow distribution. Traditionally, most of theoretical models are based on Bernoulli equation after taking the frictional losses into account using a control volume (Fig. 2).
Minor losses in pipe flow are a major part in calculating the flow, pressure, or energy reduction in piping systems. Liquid moving through pipes carries momentum and energy due to the forces acting upon it such as pressure and gravity.
The Fanning friction factor (named after American engineer John T. Fanning) is a dimensionless number used as a local parameter in continuum mechanics calculations. It is defined as the ratio between the local shear stress and the local flow kinetic energy density: [1] [2]
This equation holds for flow through packed beds with particle Reynolds numbers up to approximately 1.0, after which point frequent shifting of flow channels in the bed causes considerable kinetic energy losses. This equation is a particular case of Darcy's law, with a very specific permeability.